Сократите дробь: 2x² + 9x +7 029.20. a) x²-1 ; 9x2 -1 6) ; 3x² - 8x - 3 ; B) 2x²+7x-4. x²-16 4x²-1 г) 2x²-9x-5 x2 8x + 15 6x219x + 13 029.21. a) ; B) x² + 7x - 30 2x²+7x-9 6x² + 7x - 3 21x2 + x2 б) ; г) 2x15x2 2+5x-3x² 029.22. Упростите выражение: 1 5 x a) (x+2+x-x-63) 2x+1 ; 2 10 3x 3x + 2 + + x + 1 x²-3x-4 x-4 3 Решите уравнение:

029.20 a)

\[\frac{2x^2 + 9x + 7}{x^2 - 1} = \frac{(2x + 7)(x + 1)}{(x - 1)(x + 1)} = \frac{2x + 7}{x - 1}\]

029.20 б)

\[\frac{9x^2 - 1}{3x^2 - 8x - 3} = \frac{(3x - 1)(3x + 1)}{(3x + 1)(x - 3)} = \frac{3x - 1}{x - 3}\]

029.20 в)

\[\frac{2x^2 + 7x - 4}{x^2 - 16} = \frac{(2x - 1)(x + 4)}{(x - 4)(x + 4)} = \frac{2x - 1}{x - 4}\]

029.20 г)

\[\frac{4x^2 - 1}{2x^2 - 9x - 5} = \frac{(2x - 1)(2x + 1)}{(2x + 1)(x - 5)} = \frac{2x - 1}{x - 5}\]

029.21 a)

\[\frac{x^2 - 8x + 15}{x^2 + 7x - 30} = \frac{(x - 3)(x - 5)}{(x - 3)(x + 10)} = \frac{x - 5}{x + 10}\]

029.21 б)

\[\frac{6x^2 + 7x - 3}{2 - x - 15x^2} = \frac{(2x + 3)(3x - 1)}{-(3x - 1)(5x + 2)} = -\frac{2x + 3}{5x + 2}\]

029.21 в)

\[\frac{6x^2 - 19x + 13}{2x^2 + 7x - 9} = \frac{(6x - 13)(x - 1)}{(2x + 9)(x - 1)} = \frac{6x - 13}{2x + 9}\]

029.21 г)

\[\frac{21x^2 + x - 2}{2 + 5x - 3x^2} = \frac{(3x + 1)(7x - 2)}{-(3x + 1)(x - 2)} = -\frac{7x - 2}{x - 2}\]

029.22 a)

\[(\frac{1}{x + 2} + \frac{5}{x^2 - x - 6} + \frac{2x}{x - 3}) \cdot \frac{x}{2x + 1} = (\frac{1}{x + 2} + \frac{5}{(x - 3)(x + 2)} + \frac{2x}{x - 3}) \cdot \frac{x}{2x + 1} = \frac{x - 3 + 5 + 2x(x + 2)}{(x - 3)(x + 2)} \cdot \frac{x}{2x + 1} = \frac{x - 3 + 5 + 2x^2 + 4x}{(x - 3)(x + 2)} \cdot \frac{x}{2x + 1} = \frac{2x^2 + 5x + 2}{(x - 3)(x + 2)} \cdot \frac{x}{2x + 1} = \frac{(2x + 1)(x + 2)}{(x - 3)(x + 2)} \cdot \frac{x}{2x + 1} = \frac{x}{x - 3}\]

029.22 б)

\[(\frac{2}{x + 1} + \frac{10}{x^2 - 3x - 4} + \frac{3x}{x - 4}) : \frac{3x + 2}{3} = (\frac{2}{x + 1} + \frac{10}{(x - 4)(x + 1)} + \frac{3x}{x - 4}) : \frac{3x + 2}{3} = \frac{2(x - 4) + 10 + 3x(x + 1)}{(x - 4)(x + 1)} : \frac{3x + 2}{3} = \frac{2x - 8 + 10 + 3x^2 + 3x}{(x - 4)(x + 1)} : \frac{3x + 2}{3} = \frac{3x^2 + 5x + 2}{(x - 4)(x + 1)} : \frac{3x + 2}{3} = \frac{(3x + 2)(x + 1)}{(x - 4)(x + 1)} : \frac{3x + 2}{3} = \frac{3}{x - 4}\]